The Cahn–Hilliard equation, first described by Cahn&Hilliard (1958), [1]}, is an equation in mathematical physics and describes the phase separation of a binary fluid. The functions \(W_\Omega ,W_\Gamma :\mathbb {R} \rightarrow \mathbb {R}\)  are chemical potentials, a typical example could be the double-well potential \(W(u)=(u^2-1)^2\) . The solution \(u\in [-1,1]\)  is the concentration of the two components of the fluid, \(u=\pm 1\)  then indicates a pure occurrence of one of the components.
The two components are mixed in the beginning and then start building segregated domains, which are changing in time. To model the interactions with the wall in confined systems, dynamic boundary conditions are introduced, which is described in Goldstein et al. (2016), [2]}.
